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Math Help - Finding two unknows from one equation

  1. #1
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    Finding two unknows from one equation

    Dear members

    I have been set a task to find n and m (two constants) in the following equation: N=(z^m).(r^n). I have been provided with data for N, z and r. I am assuming that I can plot this data to find m and n, but I am unsure on how to rearrange the equation to achieve this. I would be appreciative of your help.

    Thanks
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  2. #2
    Senior Member Twig's Avatar
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     N = z^{m} \cdot r^{n}

     ln(N) = ln(z^{m} \cdot r^{n}) = m\cdot ln(z) + n\cdot ln(r)

    If we let  ln(z) = x \mbox{ and } ln(r) = y \mbox{ and } ln(N)=c , then

     \left[ \begin{matrix} m\cdot x_{1} & n\cdot y_{1} \\ m\cdot x_{2} & n\cdot y_{2} \end{matrix}\right] = \left[ \begin{matrix} x_{1} & y_{1} \\ x_{2} & y_{2} \end{matrix}\right] \, \left[ \begin{matrix} m \\ n \end{matrix} \right]
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